Remove stems from shiitake mushrooms; discard. Slice shiitake mushroom caps; set aside.
Heat oil in a large nonstick skillet over medium heat. Add ginger, chili paste, and garlic; sauté 1 minute. Add shiitake mushroom caps, button mushrooms, and portobello mushrooms; sauté 3 minutes. Add remaining ingredients; cook 1 minute or until sauce thickens. Serve warm, at room temperature, or chilled.